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Trick Question?

by Rastis » Tue Mar 24, 2015 7:46 am
A couple has two children, one of whom is a girl. If the probability of having a girl or a boy is 50%, what is the probability that the couple has two daughters?

a) 1/8

b) 1/4

c) 1/3

d) 1/2

e) 2/3

I believe the answer is B, while the explanation says C. The explanation lists BG, GB and GG as their combinations. However, aren't they double counting with BG and GB?
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by Brent@GMATPrepNow » Tue Mar 24, 2015 8:00 am
Rastis wrote:A couple has two children, one of whom is a girl. If the probability of having a girl or a boy is 50%, what is the probability that the couple has two daughters?

a) 1/8
b) 1/4
c) 1/3
d) 1/2
e) 2/3
If we list the possibilities in the form "1st child - 2nd child," the 4 possible cases are:
B-B
B-G
G-B
G-G

We're told that at least one of the children is a girl. In other words, the couple has one of these 3 EQUALLY-LIKELY cases:
B-G
G-B
G-G

The question asks for the probability of G-G, so the probability = [spoiler]1/3[/spoiler]

Answer: C

Cheers,
Brent
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by Rastis » Tue Mar 24, 2015 8:11 am
Brent,

But the question doesn't call for a combination. If you have already identified BG as a possibility, then adding GB is creating something different.
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by regor60 » Tue Mar 24, 2015 9:25 am
Rastis wrote:Brent,

But the question doesn't call for a combination. If you have already identified BG as a possibility, then adding GB is creating something different.
OK, but if you limit this to BB, GB and GG, then you have to acknowledge that the GB combination is twice as likely to occur relative to either the BB or GG combinations. In other words, 50% vs 25% for either.

So with a girl being at least one of the children, the choices are limited to BG and GG, at 50% and 25% likelihood respectively. Therefore, the GG combination comprises 25% of the 75% probability of either occurring, or 1/3.
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by Brent@GMATPrepNow » Tue Mar 24, 2015 4:11 pm
Rastis wrote:Brent,

But the question doesn't call for a combination. If you have already identified BG as a possibility, then adding GB is creating something different.
Having a girl 1st and a boy 2nd is different from having a boy 1st and a girl 2nd.

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by ceilidh.erickson » Sat Mar 28, 2015 4:14 pm
The wording of this question is misleading and not at all GMAT-like. The question states "the probability of having a girl or a boy is 50%." In the real world, we're perfectly aware of what the author meant, but as written this actually implies that there's a 50% chance of having one of the two - a boy or a girl - and a 50% chance of having something else. A goat? A shoe? We have no idea.

It's also very un-GMAT-like to pose a question that in other circumstances could have other answers. By itself, the question "what is the probability that the couple has two daughters?" should yield the answer 1/4. If the writer wanted to take into account the constraint that one of the children is known to be a girl, the question should have been phrased "if one of the children is a girl, what is the probability that both children are girls?"

I would just ignore this question.
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by Rastis » Mon Mar 30, 2015 5:19 am
Thank, you, Ceilidh! Your explanation is exactly what I was trying to convey.
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by Testtrainer » Thu Apr 02, 2015 10:12 am
This question is indeed too advanced for the GMAT. It actually tests an abstract concept in Probability sometimes known as the Monty Hall problem (from Lets Make a Deal). It goes like this: You're on Lets Make a Deal and are asked to choose one out of three curtains, one which has a car behind it, the other two have goats. Suppose you choose Curtain #1. Monty then tells you that Curtain #2 has a goat behind it and that you may switch your choice to Curtain #3. The question: should you choose Curtain #3 or would it make no difference whether you stay with Curtain #1? The answer: you should switch, because then theoretically you would have a 2/3 of chance of winning versus only 1/2. But here's where things get really bizarre (which is why it wouldn't be on the GMAT), long-term random selections yield roughly 70% for Curtain #3 with the car and 30% for Curtain #1. But the math works out to 66.67% and 33.33%. It has something to do with the laws of large numbers, a concept certainly not on the GMAT. Just sayin'.
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by Amrabdelnaby » Sun Nov 15, 2015 7:21 am
I concluded that the probability is half because order here doesn't matter. isn't B-G the same as G-B?


Brent@GMATPrepNow wrote:
Rastis wrote:A couple has two children, one of whom is a girl. If the probability of having a girl or a boy is 50%, what is the probability that the couple has two daughters?

a) 1/8
b) 1/4
c) 1/3
d) 1/2
e) 2/3
If we list the possibilities in the form "1st child - 2nd child," the 4 possible cases are:
B-B
B-G
G-B
G-G

We're told that at least one of the children is a girl. In other words, the couple has one of these 3 EQUALLY-LIKELY cases:
B-G
G-B
G-G

The question asks for the probability of G-G, so the probability = [spoiler]1/3[/spoiler]

Answer: C

Cheers,
Brent
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by Amrabdelnaby » Sun Nov 15, 2015 7:21 am
I concluded that the probability is half because order here doesn't matter. isn't B-G the same as G-B?


Brent@GMATPrepNow wrote:
Rastis wrote:A couple has two children, one of whom is a girl. If the probability of having a girl or a boy is 50%, what is the probability that the couple has two daughters?

a) 1/8
b) 1/4
c) 1/3
d) 1/2
e) 2/3
If we list the possibilities in the form "1st child - 2nd child," the 4 possible cases are:
B-B
B-G
G-B
G-G

We're told that at least one of the children is a girl. In other words, the couple has one of these 3 EQUALLY-LIKELY cases:
B-G
G-B
G-G

The question asks for the probability of G-G, so the probability = [spoiler]1/3[/spoiler]

Answer: C

Cheers,
Brent
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